Multivariate Skew-Normal Individual Excess-of-Loss Reserving

In excess-of-loss reinsurance, only claims with incurred loss above a reporting threshold speci_ed in the treaty are noti_ed to the reinsurer. The data available for reinsurance pricing and reserving are, thus, incomplete and failing to account for this limitation may bias the actuarial analysis. The collective approach based on aggregate development triangles cannot deal with this kind of incompleteness. This is why we develop here an individual reserving method combining paid and incurred losses which can cope with any non-proportional reinsurance treaty. Extensive numerical illustrations performed on a motor third party liability reinsurance data set demonstrate the relevance of the approach proposed in this paper.